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A112205 McKay-Thompson series of class 72a for the Monster group. 2
1, 1, 1, 0, 1, 2, 2, 2, 3, 4, 4, 4, 5, 7, 7, 8, 10, 12, 14, 14, 17, 20, 22, 24, 28, 33, 36, 40, 45, 52, 56, 62, 71, 80, 88, 96, 109, 122, 133, 144, 163, 182, 198, 216, 240, 268, 290, 316, 349, 386, 420, 456, 502, 552, 600, 650, 713, 780, 846, 916, 1001, 1093, 1182 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(5/4)*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Nov 12 2015

Expansion of q^(1/2)*(eta(q^2)*eta(q^3)^2*eta(q^12)^2*eta(q^18)/(eta(q) *eta(q^4)*eta(q^6)^2*eta(q^9)*eta(q^36))) in powers of q. - G. C. Greubel, Jun 16 2018

EXAMPLE

T72a = 1/q + q + q^3 + q^7 + 2*q^9 + 2*q^11 + 2*q^13 + 3*q^15 + 4*q^17 + ...

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[(1+x^k) * (1-x^(3*k))^2 * (1+x^(6*k))^2 * (1+x^(9*k)) / ((1-x^(4*k)) * (1-x^(36*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 12 2015 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; e72a:= q^(1/2)*((eta[q^2]*eta[q^3]^2 *eta[q^12]^2*eta[q^18])/(eta[q]*eta[q^4]*eta[q^6]^2*eta[q^9]*eta[q^36])); a[n_]:= SeriesCoefficient[e72a, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 18 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^3)^2*eta(q^12)^2*eta(q^18)/( eta(q)*eta(q^4)*eta(q^6)^2*eta(q^9)*eta(q^36))); Vec(A) \\ G. C. Greubel, Jun 16 2018

CROSSREFS

Sequence in context: A294621 A029077 A112176 * A117953 A128331 A084827

Adjacent sequences:  A112202 A112203 A112204 * A112206 A112207 A112208

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 20 04:43 EST 2019. Contains 319323 sequences. (Running on oeis4.)